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| 含时线性势Gross-Piteavskii方程的孤立波解 | |
| 引用本文： | 石玉仁,许新建,吴枝喜,汪映海,杨红娟,吕克璞,段文山.含时线性势Gross-Piteavskii方程的孤立波解[J].兰州大学学报(自然科学版),2007,43(4):131-135. |
| 作者姓名： | 石玉仁 许新建 吴枝喜 汪映海 杨红娟 吕克璞 段文山 |
| 作者单位： | 1. 兰州大学,理论物理研究所,甘肃,兰州,730000;西北师范大学,物理与电子工程学院,甘肃,兰州,730070 2. 兰州大学,理论物理研究所,甘肃,兰州,730000 3. 西北师范大学,物理与电子工程学院,甘肃,兰州,730070 |
| 摘 要： | 首先对双曲函数法进行了扩展,使其可用于求解变系数非线性演化方程,然后用此方法成功得到了Gross-Pitaevskii方程在某含时线性势下的两类精确解.结果表明在吸引势情形下,方程存在钟形包络孤立波解;在排斥势情形下,存在扭结形包络孤立波解.该方程可用来描述重力场中在随时间变化的外磁场作用下的玻色-爱因斯坦凝聚体的演化过程,故所得解具有重要的物理意义. |
| 关 键 词： | Gross-Piteavskii方程 扩展双曲函数法 精确解 孤立波解 |
| 文章编号： | 0455-2059（2007）04-0131-05 |
| 修稿时间： | 2005-06-132006-10-16 |
Exact solitary wave solutions for the Gross-Piteavskii equation with time-dependent linear potential |
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| SHI Yu-ren,XU Xin-jian,WU Zhi-xi,WANG Ying-hai,YANG Hong-juan,L Ke-pu,DUAN Wen-shan.Exact solitary wave solutions for the Gross-Piteavskii equation with time-dependent linear potential[J].Journal of Lanzhou University(Natural Science),2007,43(4):131-135. | |
| Authors: | SHI Yu-ren XU Xin-jian WU Zhi-xi WANG Ying-hai YANG Hong-juan L Ke-pu DUAN Wen-shan |
| Institution: | 1. Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China; 2. School of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China |
| Abstract: | We extended the hyperbolic function method for solving the nonlinear evolution equations with variable coefficients. By using this method, we derived two types of exact solutions to the Gross-Pitaevskii equation with time-dependent linear potential. The results indicated that the equation has bell-like envelope solution when the potential is attracted while it has kink envelope solution when the potential is repelled. Because the Gross-Pitaevskii equation can be used to describe the process of Bose-Einstein condensation in gravity field and magnetic field, the solutions we obtained are physically important. |
| Keywords: | Gross-Piteavskii equation extended hyperbolic function method exact solution solitary wave solution |
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